Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(1) \cdot (5 e^{4\pi i / 3})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $1$ ) has angle $0$ and radius $1$ The second number ( $5 e^{4\pi i / 3}$ ) has angle $\frac{4}{3}\pi$ and radius $5$ The radius of the result will be $1 \cdot 5$ , which is $5$ The angle of the result is $0 + \frac{4}{3}\pi = \frac{4}{3}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{4}{3}\pi$.